References
N. G. de Bruijn,Gemeenschappelijke representatennsystemen van twee klassenindelingen van een verzameling, Niew Archief voor Wiskunde22 (1947), 48–52.
C. C. Chang,Cardinal and ordinal factorization of relation types, Proceedings of Symposia in Pure Mathematics, vol. 2, Lattice Theory, Amer. Math. Soc. (1961), 123–128.
C. C. Chang, B. Jónsson and A. Tarski,Refinement properties for relational structures, Fund. Math.55 (1964), 249–281.
C. C. Chang,Cardinal factorization of finite relational structures, Fund. Math.60 (1967), 251–269.
A. H. Clifford and G. B. Preston,The algebraic theory of semigroups, Volume I, Mathematical Surveys, No. 7, Amer. Math. Soc., 1961.
A. L. S. Corner,Additive categories and a theorem of Leavitt, Bull. Amer. Math. Soc.75 (1969), 78–82.
Peter Crawley and Bjarni Jónsson, RefRefinements for infinite direct decompositions of algebraic systems, Pacific J. Math.14 (1964), 797–855.
Bjarni Jónsson,The unique factorization problem for finite relational structures, Colloq. Math.14 (1966), 1–32.
B. Jónsson and A. Tarski,Direct decompositions of finite algebraic systems, Notre Dame Mathematical Lectures, No. 5, 1947.
W. Imrich and W. Dörfler,Über das starke Produkt von endlichen Graphen, Sitzungsberichte der Österreichischen Akademie der Wissenschaften Mathem.=naturw. Klasse, II (about 1971).
László Lovász,Operations with structures, Acta Math. Acad. Sci. Hung.18 (1967), 321–328.
László Lovász,On the cancellation law among finite relational structures, Periodica Mathematica Hungarica1 (1971), 145–156.
Ralph McKenzie,On finite groupoids and K-prime algebras, Trans. Amer. Math. Soc.133 (1968), 115–129.
Ralph McKenzie,Cardinal multiplication of structures with a reflexive relation, Fund. Math.70 (1971), 59–101.
Ralph Seifert, Jr.,On prime binary relational structures, Fund. Math.70 (1971), 187–203.
Ladislav Skula,Prime elements in the semigroup of finite types of partially ordered sets in cardinal multiplication, Spisy přírodovědecké fakulty Univ. J. E. Purkyně v Brně (Czechoslovakian) T4 (1968), 97–102.
Alfred Tarski,On direct products of Boolean algebras with additional operations, Notices Amer. Math. Soc.13 (1966), 728–729 (Abstract).
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McKenzie, R. A method for obtaining refinement theorems, with an application to direct products of semigroups. Algebra Univ. 2, 324–338 (1972). https://doi.org/10.1007/BF02945043
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DOI: https://doi.org/10.1007/BF02945043